A236509 - OEIS

%I #5 Jan 27 2014 08:42:21

%S 5,11,107,227,311,347,821,857,1091,1607,1997,2657,3527,4931,5231,8087,

%T 8231,9431,10331,11171,12917,13691,13877,21377,22271,24917,27737,

%U 29567,32057,33347,35591,36467,37307,39227,42017

%N Primes p with p + 2, p + 6 and prime(p) + 6 all prime.

%C According to the conjecture in A236508, this sequence should have infinitely many terms.

%H Zhi-Wei Sun, <a href="/A236509/b236509.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 5 since 5, 5 + 2 = 7, 5 + 6 = 11 and prime(5) + 6 = 17 are all prime, but 2 + 2 = 4 and 3 + 6 = 9 are both composite.

%t p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[n+6]&&PrimeQ[Prime[n]+6]

%t n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10^6}]

%Y Cf. A000040, A022004, A023201, A046117, A236464, A236508.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 27 2014